in some books it says in dynamics torque must always be calculated about centre of mass?

Also is it true that a body when tries to rotate always rotates about centre of mass ie axis of rotation always pass through it. I think it may be because a body free to rotate has least I about O .

Also when a body rotates around some other object each particle of body is moving with different radius and hence has different velocities so how can this happen is body in translation or rotation and how is torque acting here eg consider planetary motion.

For last one : When any object say O (which is a rigid body having appreciable dimension wrt its orbit) is rotating about a fixed point C at centre of circular orbit then according to me the bady is not just translating but it is doing both translation and rotation simaltaneously as the points the particles are basically moving in circles with their centre on C but different particles have different radius of orbit as body has size hence different velocoties therefore not in pure translation so how is this possible ? How is a free body rotating about a external point not about centre of mass

  • $\begingroup$ Also read related question: physics.stackexchange.com/a/81078/392. It answers your first question. $\endgroup$ Commented Apr 28, 2017 at 4:10
  • $\begingroup$ Any on why always use center of mass? See this question $\endgroup$ Commented Apr 28, 2017 at 4:13
  • $\begingroup$ And the second question ? It is no where related to the supposed duplicate $\endgroup$
    – Matt
    Commented Apr 28, 2017 at 11:39
  • $\begingroup$ I believe this answer to you answered this. For a body to rotate not about the COM there has to be a net force applied to it. This can be external, or a reaction from a pin joint. $\endgroup$ Commented Apr 28, 2017 at 11:45
  • $\begingroup$ No what kind of motion is of earth when it is revolving around the sun ? $\endgroup$
    – Matt
    Commented Apr 28, 2017 at 11:46